Physics What is the acceleration of the sled?

Question

Parrot and Pirate are sliding down a 30 degree hill on a 3 kg sled. The force of friction is 131 and the mass of parrot 2 kg, while pirate is 71 kg. What is the acceleration of the sled?

Answer 1

Hi Hannah.

 

If Pirate (71  kg), parrot (2 kg), and sled (3 kg) are all together, you have a total mass of 76kg sliding down this incline plane.

 

If you draw the free body diagram, you'll have (mg) pointing straight down, and a normal force pointing perpendicular to the plane. Friction will be parallel to the plane in the opposite direction of the motion.

 

The Normal force will be balanced by mg*cos(theta).

 

The Friction force will be balanced by mg*sin(theta).

 

You know the friction is 131 (I'm assuming Newtons). You also know that the sum of the forces acting along the plane is equal to m*a. We'll assume the direction of motion is positive.

 

So

 

∑F_plane = mg*sin(theta) - 131 N = m*a

 

(76kg)(9.8 m/s^2)*sin(30) - 131 N = (76kg)*a

 

372.4 N - 131 N = 76kg*a

 

241.4 N = 76kg*a

 

a = 241.4 N / 76 kg

 

a = 3.18 m/sec^2

 

Hope this helps.